In dozens of darkened rooms in cities across Asia, you will find next year's box office hits taking shape. Animation studios throughout the region house hundreds of works in progress on behalf of the biggest names in entertainment, from Disney to DreamWorks and Warner Bros. Market research firm Digital Vector estimates that last year Western studios commissioned $2 billion in animation contracts from studios predominantly in China, India, the Philippines, South Korea, Taiwan and Vietnam.

But for all that Asian input, animated films inevitably "feel" Western. That's because the Western studios dominate the creative process, typically providing the...